## 1. Introduction

[2] For several decades operational data from submarines have formed the primary basis of our observational knowledge of arctic sea-ice thickness. At first scientists used these data to characterize ice topography (pressure ridge statistics and the ice thickness distribution) and to characterize variability. By the 1980s enough data had accumulated to allow the spatial field of draft to be estimated, but it was clear that the contour maps had small-scale structure and seasonal differences affected by undersampling in both space and time [*Bourke and Garrett*, 1987; *Bourke and McLaren*, 1992]. Investigators began to use submarine data in about 1989 to address the question of interannual change. Because the timing and tracks of submarine cruises were designed to meet military objectives and not to provide optimal sampling of the spatial and temporal variability of sea ice, formulating analyses of the sparse and irregular data, either to map the field or to find a trend, has been problematic. There has been controversy about whether the data set is sufficiently strong to distinguish any signal of long-term change from “natural variability” [*McLaren et al.*, 1990; *Wadhams*, 1990]. Some studies have ignored the time of year altogether. Some have segregated the data into summer or winter seasons, ignoring the facts that summer and winter data are related via the annual cycle and that the data are spread over seven months of the year. Some have focused on certain data-rich regions such as the North Pole or the strip from the pole to the Beaufort Sea roughly between 140° and 150°W. Some have compared data from two different clusters of years. Investigations focused on interannual change include *McLaren et al.* [1992], *Shy and Walsh* [1996], *Rothrock et al.* [1999], *Tucker et al.* [2001], *Winsor* [2001], and *Wadhams and Davis* [2000]. Table 1 summarizes some of the examinations of submarine ice draft data for signs of interannual change. Unanswered questions from these studies include, “Is the interannual signal truly discernible above the noise of 'natural variability'?” and, if so, “Is the interannual change one of continual decline or is the signal more complicated?”.

Reference | # of Cruises | Years Studied |
---|---|---|

NORTH POLE | ||

McLaren et al. [1992] | 6 | 1977–1990 |

McLaren et al. [1994] | 12 | 1958–1992 |

Shy and Walsh [1996] | 12 | 1977–1992 |

FRAM STRAIT &LINCOLN SEA | ||

Wadhams [1990] | 2 | 1976 cf. 1987 |

Wadhams and Davis [2000] | 2 | 1976 cf. 1996 |

BEAUFORT SEA TO NORTH POLE | ||

McLaren [1989] | 2 | 1958 cf. 1970 |

Tucker et al. [2001] | 9 | 1976–1994 |

Winsor [2001] | 6 | 1991–1997 |

SUBMARINE DATA RELEASE AREA (DRA) | ||

Rothrock et al. [1999] | 9 | 1958–76 cf. 1993–97 |

Present | 34 | 1975–2000 |

[3] Over the decades, more and more data have become publicly available. Data on sea-ice draft from 34 U.S. Navy submarine cruises and two British cruises within the Arctic Ocean are now available at the *National Snow and Ice Data Center* [*NSIDC*, 2006]. The archived data consist of draft profiles at nominally one-meter spacing; there are on the order of 10^{8} data points (100,000 km of profiles), along with summary statistics including the mean draft over roughly 50-km sections. The purpose of this paper is to analyze these mean draft data and determine what they reveal about sea-ice variability. We purposely avoid any use here of other sea-ice information, in particular, from sea-ice models. This analysis rests purely on the submarine data and has two strengths. First, the study makes use of data from 17 cruises recently placed at NSIDC [*Wensnahan et al.*, 2007; *Rothrock and Wensnahan*, 2007], providing a fairly continual record in both spring and autumn from 1975 to 2000 from the total of 34 U.S. cruises. Second, it capitalizes on the opportunity provided by this expanded data set to analyze all the U.S. submarine data as a single data set in order to separate the dependencies on space, on season, and on year. In taking this approach we begin to fulfill the vision of *McLaren et al.* [1990] who saw that “A direct approach would involve statistical analysis by season, region and … for each year of all…under-ice thickness distribution data obtained by U.S. and British nuclear submarines since 1958. Only then might genuine trends be distinguished from natural variability.” We would add that only then will a spatial climatological field and annual cycle be identified.

[4] We use multiple regression to determine how draft depends on the independent variables. The goal is to find a simple algebraic formula or regression model for draft as a function of space, season, and year, leaving residuals (discrepancies between the data and the regression model) that are small. We build the regression model by starting with terms of low order and adding terms of higher order, until the addition ceases to reduce the variance of the residuals significantly as determined by statistical tests. The regression model “explains” a portion of the variance in the data, leaving the remaining variance in the residuals as “unexplained” variance that can be considered as either error in the regression model or observational error or both. We adopt a regression model in which the spatial, annual, and interannual variations are separated and additive. Of course this form is somewhat subjective, guided by physical intuition, but, for instance, whether the spatial dependence should be linear or quadratic or cubic is determined by the data.

[5] In section 2, the data set is described and the variables defined. Section 3 presents the best fit multiple regression model and the coefficients of the fit: the seasonal cycle, the spatial field, and the interannual change. Section 4 gives the relationship between ice draft and the combined mass of sea ice plus its snow cover and suggests that this observed ice-cover (ice-plus-snow) mass may be worth using to test models. Section 5 gives the relationship between draft and ice thickness. In section 6 these results are discussed in the context of previous results.